Stability and Robustness of RBF Interpolation

TL;DR

This paper investigates the stability and robustness of RBF interpolation, especially general multiquadrics, under noise, introducing FFT-based methods for improved interpolation on bounded domains.

Contribution

It presents new FFT-based approaches for RBF interpolation on bounded domains, enhancing stability and robustness analysis under noisy conditions.

Findings

FFT methods improve interpolation efficiency

Multiquadric RBFs show robustness to noise

New techniques extend interpolation capabilities on bounded domains

Abstract

We consider how some methods of uniform and nonuniform interpolation by translates of radial basis functions -- specifically the so-called general multiquadrics -- perform in the presence of certain types of noise. These techniques provide some new avenues for interpolation on bounded domains that is different from the existing literature by using fast Fourier transform methods to approximate cardinal functions associated with the RBF.